Velocity selection problem in the presence of the triple junction

Melting of a bicrystal along the grain boundary is discussed. A triple junction plays a crucial role in the velocity selection problem in this case. In some range of the parameters an entirely analytical solution of this problem is given. This allows us to present a transparent picture of the structure of the selection theory. We also discuss the selection problem in the case of the growth of a "eutectoid dendrite."     

Functional limit theorems for the maxima of perturbed random walk and divergent perpetuities in the <Emphasis Type="Italic">M</Emphasis><Subscript>1</Subscript>-topology

Let (ξ ₁, η ₁), (ξ ₂, η ₂),… be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the J ₁-topology on the Skorokhod space of \(n^{-1/2}\underset {0\leq k\leq [n\cdot ]}{\max }\,(\xi _{1}+\ldots +\xi _{k}+\eta _{k+1})\) was proved under the assumption that contributions of \(\underset {0\leq k\leq n}{\max }\,(\xi _{1}+\ldots +\xi _{k})\) and \(\underset {1\leq k\leq n}{\max }\,\eta _{k}\) to the limit are comparable and that n ^?1/2(ξ ₁+… + ξ _[n?]) is attracted to a Brownian motion. In the present paper, we continue this line of research and investigate a more complicated situation when ξ ₁+… + ξ _[n?], properly normalized without centering, is attracted to a centered stable Lévy process, a process with jumps. As a consequence, weak convergence normally holds in the M ₁-topology. We also provide sufficient conditions for the J ₁-convergence. For completeness, less interesting situations are discussed when one of the sequences \(\underset {0\leq k\leq n}{\max }\,(\xi _{1}+\ldots +\xi _{k})\) and \(\underset {1\leq k\leq n}{\max }\,\eta _{k}\) dominates the other. An application of our main results to divergent perpetuities with positive entries is given.     

Elastic properties of compressed rare-gas crystals in a model of deformable atoms

Physics of the Solid State - The elastic properties of compressed Ne, Ar, Kr, and Xe rare-gas crystals were studied in a model of deformable and polarizable atoms. The second-order Fuchs elasticity...     

Selectivity and sensitivity of metal determination by co-ordination compounds

Quantum chemical structure calculations for metal co-ordination compounds with various organic ligands allow choice of generalized parameters of chelate electronic structures, to form a basis for systematization and prediction of analytical properties. The extent of the co-ordinative saturation of a metal is measured as the sum of the covalent bonding energies of the two-centre metal interactions with the ligand atoms. The concept of "valence state of the ligand" is considered and characterized by the energy sum of the covalent components of two-centre interactions in the ligand. It is shown that the ligand structure can be correlated with the complex stability and this provides a new mechanism for assessing the influence of substituents in ligands. The calculated data make it possible to predict compound stability in solutions and synergic action, and therefore such analytical properties as sensitivity and selectivity. For the azo dyes as an example, it is shown that quantum chemical calculations can explain many of the experimental data on the use of azo dyes in photometry, and suggest directions of search for new analytical reagents.     

The Nordheim Function in an Array of Homogeneous Identical Nanotubes under Field Emission

Technical Physics - The problem of field emission based on carbon nanotubes is considered. The particle transmission function is obtained. The dependence of the Nordheim function on the length of...     

Oxidative Conversion of Wood Gasification Products in a Mixing Reactor

Russian Journal of Applied Chemistry - The results of thermodynamic calculations and experimental data on conversion of wood gasification tars in pyrolysis gas to tar-free fuel gas by partial...     

Elastic properties of compressed crystalline Ne in the model of deformable atoms

An ab initio version of the model with deformable atoms has been constructed to investigate the elastic properties of compressed crystalline neon. Approximations for the calculating parameters of quadrupole deformation of atomic electron shells have been discussed. It has been shown that the pressure dependence of the deviation from the Cauchy relation δ is the result of two competitive interactions, namely, the many-body and electron-phonon interactions, which manifests itself in the deformation of atomic electron shells during the shift of nuclei. In the case of Ne, contributions of these interactions are compensated to a large degree, which provides a weakly pressure-dependent positive value for δ. The agreement of calculated elastic moduli and deviations from the Cauchy relation for Ne with the experiment is good.